A148170 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 1), (-1, 1, 1), (0, 0, 1), (0, 1, -1), (1, -1, 0)}.

1, 1, 2, 4, 11, 32, 101, 335, 1160, 4173, 15440, 58553, 226598, 892671, 3571202, 14476138, 59374785, 246066600, 1029190063, 4340404260, 18441133536, 78878447049, 339449124384, 1468928554576, 6388963314642, 27917807301818, 122516036588009, 539786210702003, 2386929090607550, 10590875213625467

Offset

0,3

Links

Table of n, a(n) for n=0..29.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A120848 A320567 A135339 * A156043 A268322 A148171

Adjacent sequences: A148167 A148168 A148169 * A148171 A148172 A148173

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved